Soy feliz

Hola Peter

It would have been absolutely correct to say "estoy feliz" here as the character is expressing a feeling at that precise moment so it implies a result, more than a permanent characteristic. But with the adjective feliz, there is a tendency to use "ser" despite this general rule, so even if we are talking about something "circumstantial" you may see feliz with ser very often.

Saludos

Inma